Molecular Simulations of Phase Transitions in Pores

Direct Observation of the Vapor-Liquid Phase Transition and Hysteresis in 2 nm Nanochannels

The characterization of fluid phase transitions in nanoscale pores remains a challenging problem that can significantly affect various applications, such as drug delivery, carbon dioxide storage, and enhanced oil recovery. Previous theoretical and experimental studies have shown that the fluid phase transition changes drastically when the fluid is confined within nanocapillaries with dimensions of <10 nm, potentially due to the dominance of fluid-surface interactions compared to bulk effects. However, due to challenges in performing experiments at the nanoscale, there have been limited experimental observations of the phase transition at this scale. Recent advances in lab-on-a-chip (LOC) technology have enabled the observation of many nanoscale phenomena. In this study, for the first time, we present the direct observation and visualization of n-butane vapor-liquid phase transitions in a 2 nm slit pore using LOC technology. Our experiments, for the first time, measured and directly visualized the deviation of the vapor-liquid phase transition pressure in a 2 nm slit pore compared to the associated unconfined or bulk value. We also measured the liquid-vapor phase transition pressure and observed a significant difference from the vapor-liquid phase transition pressure. We complemented our experimental observations with grand canonical ensemble Monte Carlo molecular simulations to understand the underlying molecular-level mechanisms.

Confinement driven anomalous freezing in nano porous spray dried microspheres

One-step evaporative jamming of colloidal silica particles in contact-free spray droplets resulted in well-defined powder micro-granules with interstitial nanopores. This paper reports the anomalous freezing behaviour of confined water in the microspheres synthesized using spray drying. It has been revealed that the freezing point of water in these microspheres gets significantly lowered (∼-45 °C) owing to the confinement effect. Thermoporometry results are corroborated with the structural details obtained using complementary techniques of gas adsorption measurements and small-angle x-ray scattering.

Virial series expansion and Monte Carlo studies of equation of state for hard spheres in narrow cylindrical pores

In this paper, the virial series expansion and constant pressure Monte Carlo method are used to study the longitudinal pressure equation of state for hard spheres in narrow cylindrical pores. We invoke dimensional reduction and map the model into an effective one-dimensional fluid model with interacting internal degrees of freedom. The one-dimensional model is extensive. The Euler relation holds, and longitudinal pressure can be probed with the standard virial series expansion method. Virial coefficients B_{2} and B_{3} were obtained analytically, and numerical quadrature was used for B_{4}. A range of narrow pore widths (2R_{p}), R_{p}<(sqrt[3]+2)/4=0.9330... (in units of the hard sphere diameter) was used, corresponding to fluids in the important single-file formations. We have also computed the virial pressure series coefficients B_{2}^{'}, B_{3}^{'}, and B_{4}^{'} to compare a truncated virial pressure series equation of state with accurate constant pressure Monte Carlo data. We find very good agreement for a wide range of pressures for narrow pores. These results contribute toward increasing the rather limited understanding of virial coefficients and the equation of state of hard sphere fluids in narrow cylindrical pores.

Equation of state for hard-sphere fluid in restricted geometry

Many practical applications require the knowledge of the equation of state of fluids in restricted geometry. We study a hard-sphere fluid at equilibrium in a narrow cylindrical pore with hard walls for pore radii R<((square root 3)+2)/4 (in units of the hard sphere diameter). In this case each particle can interact only with its nearest neighbors, which makes possible the use of analytical methods to study the thermodynamics of the system. Using a transfer operator formalism and expanding in low- and high-pressure regions, we can obtain a simple analytical equation of state for almost all ranges of pressure. The results agree with Monte Carlo simulations. Additionally, it is shown that a convenient analytical representation can be chosen to accurately describe the equation of state within the error of the Monte Carlo simulation.

Grand canonical Monte Carlo simulation for determination of optimum parameters for adsorption of supercritical methane in pillared layered pores

A grand canonical Monte Carlo (GCMC) method is carried out to determine optimum adsorptive storage pressures of supercritical methane in pillared layered pores. In the simulation, the pillared layered pore is modeled by a uniform distribution of pillars between two solid walls. Methane is described as a spherical Lennard-Jones molecule, and Steele's 10-4-3 potential is used for representing the interaction between the fluid and a layered wall. The site-site interaction is also used for calculating the interaction energy between methane molecules and pillars. An effective potential model that reflects the characteristics of a real pillared layered material is proposed here. In the model, a binary interaction parameter, k(fw), is introduced into the combining rule for the cross-energy parameter for the interaction between the fluid and a layered wall. Based on the experimental results for the Zr-pillared material synthesized and characterized by Boksh, Kikkinides, and Yang, the binary interaction parameter, k(fw), is determined by fitting the simulation results to the experimental adsorption data of nitrogen at 77 K. Then, by taking it as a model of pillared layered material, a series of GCMC simulations have been carried out. The excess adsorption isotherms of methane in a pillared layered pore with three different pore widths and porosities are obtained at three supercritical temperatures T=207.3, 237.0, and 266.6 K. Based on the simulation results at different porosities, various pore widths and different supercritical temperatures, the pillared layered pore with porosity psi=0.94 and pore width hsigma(p)=1.02 nm is recommended as adsorption storage material of supercritical methane. Moreover, the optimum adsorption pressure is determined at a given temperature and a fixed width of the pillared layered pore. For example, at temperature T=207.3 K, the optimum adsorption pressures are 3.1, 3.7, and 4.5 M Pa at H=1.02, 1.70, and 2.38 nm, respectively. In summary, the GCMC method is a useful tool for optimizing adsorption storage of supercritical methane in pillared layered material.